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On the prime graph question for integral group rings of 4-primary groups I

Journal Contribution - Journal Article

We study the Prime Graph Question for integral group rings. This question can be reduced to almost simple groups by a result of Kimmerle and Konovalov. We prove that the Prime Graph Question has an affirmative answer for all almost simple groups having a socle isomorphic to PSL(2,pf) for f≤2, establishing the Prime Graph Question for all groups where the only non-abelian composition factors are of the aforementioned form. Using this, we determine exactly how far the so-called HeLP method can take us for (almost simple) groups having an order divisible by at most four different primes.
Journal: International Journal of Algebra & Computation
ISSN: 0218-1967
Issue: 6
Volume: 27
Pages: 731-767
Publication year:2017
Keywords:Integral group ring, almost simple groups, prime graph question, projective special linear group, torsion units
CSS-citation score:2
Authors:Regional
Accessibility:Closed